# Questions tagged [young-tableaux]

For standard Young tableaux, semistandard Young tableaux, and other related two-dimensional arrays of numbers like plane partitions. Including their combinatorial theory and their application in representation theory and algebraic geometry.

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### Two majs for standard Young tableaux?

Let $\lambda$ be a partition of $n$, and consider its set of standard Young tableaux (SYTs): bijective fillings of the Young diagram of $\lambda$, written in English notation, with the numbers $1$ ...
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### Cylindric partitions for lattice paths with a weight of binomial form

In Cylindric partitions prop.1, Gessel and Krattenthaler prove a formula for lattice paths on a cylinder In our particular problem, we again have paths $((P_{1},k_{1}),...,(P_{r},k_{r}))$ and the ...
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### LGV scheme for lattice paths that move in non-unit spatial positive steps

In the Lindström–Gessel–Viennot lemma (LGV) applied to the $Z^2$-lattice paths are taken to move in unit spatial-steps in unit time (see here). What do we mean by "time"? In the language of ...
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### A question related to Young symmetrizers

Let $T$ be an arbitrary Young tableau (i.e., filling of the diagram of an integer partition $\lambda$ of $n$ by the numbers from $1$ to $n$, each appearing once). Let $R(T)$ be the subgroup of ...
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### The distribution of amajor over standard Young tableaux?

Given a standard Young tableau $T$, $i$ is called an ascent of $T$ if $i+1$ is in a higher row than $i$, and amajor$(T)$ is defined to be the sum of ascents of $T$. For the distribution of the amajor ...
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### RSK correspondence for sum of two matrices

The celebrated RSK correspondence (see Wikipedia page) assigns to each integer $X$ matrix a pair of Young tableaux $P$ and $Q$. Now suppose that we have three integer matrices $X_1$, $X_2$, and $X_3$, ...
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### A basic question about Young symmetrizers

This is probably elementary for experts on the representation theory of the symmetric group, but I did not find the answers I need by a cursory look at the usual textbooks (they could be there, but I ...
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### How to represent the even signed permutations by Young tableaux?

The well-known RSK correspondence established the connection between table pair (P,Q) and the permutations in symmetry group Sn(Coxeter group of type A). Also, there is a similar correspondence for ...
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### Bijection between noncrossing matchings on $2b$ points and Standard Young Tableaux of size $2 \times b$

I'm currently reading a review article called Dynamical Algebraic Combinatorics: Promotion, Rowmotion, and Resonance by Jessica Striker. In this article, Striker writes that there is a ''nice'' ...
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### Nekrasov Partition Function: $F^{inst}(\epsilon_1,\epsilon_2,\mathbf{a},\mathbf{q})$ analytic at $\epsilon_1 = \epsilon_2 = 0$?

Nakajima & Yoshioka  showed that \begin{equation} F^{inst}(\epsilon_1,\epsilon_2,\mathbf{a},\mathbf{q}) = \sum_{n = 1}^\infty \mathbf{q}^nF^{inst}_n(\epsilon_1,\epsilon_2,\mathbf{a}) := \...
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### Is the Ford-Fulkerson algorithm a tropical rational function?

The Ford-Fulkerson algorithm Let me recall the standard scenario of flow optimization (for integer flows at least): Let $\mathbb{N} = \left\{0,1,2,\ldots\right\}$. Consider a digraph $D$ with vertex ...